A wall of a cold room consists of a layer of extruded polysterene foam $($XPS$)$ sandwiched between an outer and inner walls, the outer wall being brick is $100$ mm thick and the inner wall being wood $19$mm thick. The interior temperature is $-18\backslash$deg C when the exterior temperature is $22\backslash$deg C and the heat flow through the wall is $7\mathrm{.}5$ W$/$m$^2.$ Take the thermal conductivity coefficients of brick at $0\mathrm{.}6$ W$/$m$\backslash$deg C and wood at $0\mathrm{.}15$ W$/$m$\backslash$deg C and $($XPS$)$ as $0\mathrm{.}03$ W$/$m$\backslash$deg C$.$

A$.)$ What is the thickness of the XPS layer? $($Answer is $151\mathrm{.}2$ mm$)$

B$.)$ What is the temperatures of the outer and inner surfaces of the XPS$?($Answers are T$2=20\mathrm{.}75\backslash$deg C and T$3=(-17\mathrm{.}05)\backslash$deg C$)$

Note: Q$=7\mathrm{.}5$ J$,$ Area$=1$ m$^2$ and time$=1$ second